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Can someone explain how to approach these types of problems

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Can someone explain how to approach these types of problems

by Osirus@VeritasPrep » Fri Jan 08, 2010 10:48 am
I understand the explanations for each, but I guess I'm more interested in learning the general approach to answering these questions when you have to determine what the variables could equal to make the answer choice correct.

If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?
A) 5
B) 5(x - y)
C) 20x
D) 20y
E) 35x


If k and x are positive integers and x is divisible by 6, which of the following CANNOT be the value of ?

A) 24k sqrt(3)
B) 24 sqrt(k)
C) 24 sqrt(3k)
D) 24 sqrt(6k)
E) 72 sqrt(k)
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by kevincanspain » Thu Jan 14, 2010 3:39 pm
osirus0830 wrote: If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?
A) 5
B) 5(x - y)
C) 20x
D) 20y
E) 35x

Each is a multiple of 5, so GCD is 5 multiplied by GCD(7x, 4y)

A) is certainly possible, as 7x and 4y could have no prime factors in possible.

C) looks easier to think about than B), so skip B

For GCD to be 20x, GCD(7x,4y) must be 4x. But how can 4x be a factor of 7x? This looks promising! If I were running out of time, I'd choose C and move on!

D) For GCD to be 20y, GCD(7x,4y) must be 4y. This seems possible (for example if x = 4y)

E) For GCD to be 35x, GCD(7x, 4y) must be 7x. Case similar to D)



If I were pressed for time, I'd choose C now. If I had extra time, I'd revisit B

Note that if y and x are consecutive integers, 5(x-y) = 5. Look for 2 consecutive integers so that x is odd, for example :GCD (7(3), 4(2)) = 1
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by Osirus@VeritasPrep » Fri Jan 15, 2010 7:50 am
Thanks, that is how MGMAT approaches it as well, it is just time consuming, so I was wondering if there was a short cut I was unaware of.
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